The fractional diffusion equation is discretized by the implicit finite difference scheme with the shifted Grünwald formula. The scheme is unconditionally stable and the coefficient matrix possesses the Toeplitz-like structure. A multigrid method is proposed to solve the resulting system. Meanwhile, the fast Toeplitz matrix-vector multiplication is utilized to lower the computational cost with only O(NlogN) complexity, where N is the number of the grid points. Numerical experiments are given to demonstrate the efficiency of the method.